How do you factor $x^{2} + 11 x - 27$ $x^2+11x-27$ ?

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Answer 1 · 2015-06-17T21:39:24

The factors can be derived from the quadratic formula as:

$x^{2} + 11 x - 27 = (x + \frac{11 + \sqrt{229}}{2}) (x + \frac{11 - \sqrt{229}}{2})$ $x^2+11x-27 = (x+(11+sqrt(229))/2)(x+(11-sqrt(229))/2)$

$x^{2} + 11 x - 27$ $x^2+11x-27$

is of the form $a x^{2} + b x + c$ $ax^2+bx+c$ with $a = 1$ $a=1$ , $b = 11$ $b=11$ and $c = - 27$ $c=-27$ .

This has discriminant $Delta$ given by the formula:

$Delta = b^2-4ac = 11^2-(4xx1xx-27)$

$=121+108 = 229$

Since this is positive but not a perfect square, the quadratic has irrational factors, which we can derive from the quadratic formula:

$x^2+11x-27 = 0$ has roots given by the formula:

$x = (-b +- sqrt(Delta))/(2a) = (-11+-sqrt(229))/2$

Hence

$x^2+11x-27 = (x+(11+sqrt(229))/2)(x+(11-sqrt(229))/2)$

How do you factor x^2+11x-27x2+11x−27x^2+11x-27?